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Register a new userOrigins of the method to determine the CKM angle $gamma$ using $B^{pm} to D K^{pm}$, $D to K_{rm S}^0pi^+pi^-$ decays
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The angle $gamma$ of the Cabibbo--Kobayashi--Maskawa unitarity triangle is a benchmark parameter of the Standard Model of particle physics. A method to determine $gamma$ from $B^{pm} to D K^{pm}$ with subsequent $D to K_{rm S}^0pi^+pi^-$ or similar multibody decays has been proven to provide good sensitivity. We review the first discussions on the use of this technique, and its impact subsequently. We propose that this approach should be referred to as the BPGGSZ method.
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We present the first model-independent measurement of the CKM unitarity triangle angle $phi_3$ using $B^{pm}to D(K_{rm S}^0pi^+pi^-pi^0)K^{pm}$ decays, where $D$ indicates either a $D^{0}$ or $overline{D}^{0}$ meson. Measurements of the strong-phase difference of the $D to K_{rm S}^0pi^+pi^-pi^0$ amplitude obtained from CLEO-c data are used as input. This analysis is based on the full Belle data set of $772times 10^{6}$ $Boverline{B}$ events collected at the $Upsilon(4S)$ resonance. We obtain $phi_3 = (5.7~^{+10.2}_{-8.8} pm 3.5 pm 5.7)^{circ}$ and the suppressed amplitude ratio $r_{B} = 0.323 pm 0.147 pm 0.023 pm 0.051$. Here the first uncertainty is statistical, the second is the experimental systematic, and the third is due to the precision of the strong-phase parameters measured from CLEO-c data. The 95% confidence interval on $phi_3$ is $(-29.7,~109.5)^{circ}$, which is consistent with the current world average.
A measurement of $CP$-violating observables is performed using the decays $B^pmto D K^pm$ and $B^pmto D pi^pm$, where the $D$ meson is reconstructed in one of the self-conjugate three-body final states $K_{mathrm S}pi^+pi^-$ and $K_{mathrm S}K^+K^-$ (commonly denoted $K_{mathrm S} h^+h^-$). The decays are analysed in bins of the $D$-decay phase space, leading to a measurement that is independent of the modelling of the $D$-decay amplitude. The observables are interpreted in terms of the CKM angle $gamma$. Using a data sample corresponding to an integrated luminosity of $9,text{fb}^{-1}$ collected in proton-proton collisions at centre-of-mass energies of $7$, $8$, and $13,text{TeV}$ with the LHCb experiment, $gamma$ is measured to be $left(68.7^{+5.2}_{-5.1}right)^circ$. The hadronic parameters $r_B^{DK}$, $r_B^{Dpi}$, $delta_B^{DK}$, and $delta_B^{Dpi}$, which are the ratios and strong-phase differences of the suppressed and favoured $B^pm$ decays, are also reported.
A new and simple procedure to measure the angle $gamma$ from $B^{pm} to pi^{pm}pi^+pi^-$ and $B^{pm} to K^{pm}pi^+pi^-$ decays using SU(3) symmetry is presented. It is based on a full Dalitz plot analysis of these decays. All diagrams, including strong and electroweak penguins, are considered in the procedure. The method is also free from final state interaction problems. The theoretical error in the extraction of $gamma$ within the method should be of the order of $10^{rm o}$ or even less. Taking into account the B-meson production in the first generation of B factories and recent measurements from CLEO, this method could bring the best measurement of $gamma$ in the next years.
A binned Dalitz plot analysis of $B^pm to D K^pm$ decays, with $D to K_S pi^+pi^-$ and $D to K_S K^+ K^-$, is performed to measure the CP-violating observables $x_{pm}$ and $y_{pm}$, which are sensitive to the Cabibbo-Kobayashi-Maskawa angle $gamma$. The analysis exploits a sample of proton-proton collision data corresponding to 3.0invfb collected by the LHCb experiment. Measurements from CLEO-c of the variation of the strong-interaction phase of the $D$ decay over the Dalitz plot are used as inputs. The values of the parameters are found to be $x_+ = (-7.7 pm 2.4 pm 1.0 pm 0.4)times 10^{-2}$, $x_- = (2.5 pm 2.5 pm 1.0 pm 0.5) times 10^{-2}$, $y_+ = (-2.2 pm 2.5 pm 0.4 pm 1.0)times 10^{-2}$, and $y_- = (7.5 pm 2.9 pm 0.5 pm 1.4) times 10^{-2}$. The first, second, and third uncertainties are the statistical, the experimental systematic, and that associated with the precision of the strong-phase parameters. These are the most precise measurements of these observables and correspond to $gamma = (62^{,+15}_{,-14})^circ$, with a second solution at $gamma to gamma + 180^circ$, and $r_B = 0.080^{+ 0.019}_{-0.021}$, where $r_B$ is the ratio between the suppressed and favoured $B$ decay amplitudes.
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